Κανόνας Born
Κανών Born Laws of physics, Born rule thumb|300px| [[Επιστημονικός Νόμος Επιστημονικοί Νόμοι ---- Μαθηματικό Θεώρημα Νόμοι Μαθηματικών ---- Φυσικός Νόμος Νόμοι Φυσικής ---- Νόμοι Χημείας ---- Νόμοι Γεωλογίας ---- Νόμοι Βιολογίας ---- Νόμοι Οικονομίας ]] thumb|300px| [[Επιστήμη Επιστήμες Φυσικές Επιστήμες Βιο-Επιστήμες Γεω-Επιστήμες Οικονομικές Επιστήμες Θεωρητικές Επιστήμες Κοινωνικές Επιστήμες Επιστήμες Υγείας ---- Τεχνολογία ---- Επιστημονικός Κλάδος Επιστημονικός Νόμος Επιστημονική Μέθοδος Επιστημονική Θεωρία Επιστημονικά Κέντρα Γης Επιστήμονες Γης ]] - Ένας Νόμος της Φυσικής. - Ακριβέστερα, είναι ένας νόμος της Κβαντικής Φυσικής - Χρονολογία ανακάλυψης. Ετυμολογία Η ονομασία "νόμος" σχετίζεται ετυμολογικά με το όνομα του φυσικού επιστήμονα " ". Διατύπωση The Born rule (also called the Born law, Born's rule, or Born's law) is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of quantum mechanics. There have been many attempts to derive the Born rule from the other assumptions of quantum mechanics, with inconclusive results. The rule The Born rule states that if an observable corresponding to a Hermitian operator A with discrete spectrum is measured in a system with normalized wave function \scriptstyle|\psi\rang (see bra–ket notation), then * the measured result will be one of the eigenvalues \lambda of A , and * the probability of measuring a given eigenvalue \lambda_i will equal \scriptstyle\lang\psi|P_i|\psi\rang , where P_i is the projection onto the eigenspace of A corresponding to \lambda_i . :(In the case where the eigenspace of A corresponding to \lambda_i is one-dimensional and spanned by the normalized eigenvector \scriptstyle|\lambda_i\rang , P_i is equal to \scriptstyle|\lambda_i\rang\lang\lambda_i| , so the probability \scriptstyle\lang\psi|P_i|\psi\rang is equal to \scriptstyle\lang\psi|\lambda_i\rang\lang\lambda_i|\psi\rang . Since the complex number \scriptstyle\lang\lambda_i|\psi\rang is known as the probability amplitude that the state vector \scriptstyle|\psi\rang assigns to the eigenvector \scriptstyle|\lambda_i\rang , it is common to describe the Born rule as telling us that probability is equal to the amplitude-squared (really the amplitude times its own complex conjugate). Equivalently, the probability can be written as \scriptstyle|\lang\lambda_i|\psi\rang|^2 .) In the case where the spectrum of A is not wholly discrete, the spectral theorem proves the existence of a certain projection-valued measure Q , the spectral measure of A . In this case, * the probability that the result of the measurement lies in a measurable set M will be given by \scriptstyle\lang\psi|Q(M)|\psi\rang . If we are given a wave function \scriptstyle\psi for a single structureless particle in position space, this reduces to saying that the probability density function p(x,y,z) for a measurement of the position at time t_0 will be given by : p(x,y,z)= |\psi(x,y,z,t_0)|^2. History The Born rule was formulated by Born in a 1926 paper. In this paper, Born solves the Schrödinger equation for a scattering problem and, inspired by Einstein's work on the photoelectric effect, concluded, in a footnote, that the Born rule gives the only possible interpretation of the solution. In 1954, together with Walther Bothe, Born was awarded the Nobel Prize in Physics for this and other work. John von Neumann discussed the application of spectral theory to Born's rule in his 1932 book. Interpretations While it has been claimed that Born's law can be derived from the Many Worlds Interpretation, the existing proofs have been criticized as circular.N.P. Landsman, "The conclusion seems to be that no generally accepted derivation of the Born rule has been given to date, but this does not imply that such a derivation is impossible in principle.", in Compendium of Quantum Physics (eds.) F.Weinert, K. Hentschel, D.Greenberger and B. Falkenburg (Springer, 2008), ISBN 3-540-70622-4 Within the Quantum Bayesianism interpretation of quantum theory, the Born rule is seen as an extension of the standard Law of Total Probability, which takes into account the Hilbert space dimension of the physical system involved.[http://arxiv.org/pdf/1003.5209v1.pdf Fuchs, C. A. QBism: the Perimeter of Quantum Bayesianism 2010 ] In the ambit of the so-called Hidden-Measurements Interpretation of quantum mechanics the Born rule can be derived by averaging over all possible measurement-interactions that can take place between the quantum entity and the measuring system. Aerts, D. (1986). A possible explanation for the probabilities of quantum mechanics, Journal of Mathematical Physics, 27, pp. 202-210.Aerts, D. and Sassoli de Bianchi, M. (2014). The extended Bloch representation of quantum mechanics and the hidden-measurement solution to the measurement problem. Annals of Physics 351, Pages 975–1025 (Open Access). Υποσημειώσεις Εσωτερική Αρθρογραφία *Επιστημονικός Νόμος *Φυσικός Νόμος *Νόμοι Διατήρησης *Νόμοι Νεύτωνα *Unitarity *Quantum non-equilibrium *Gleason's theorem *Transactional interpretation of quantum mechanics *Hidden-measurements interpretation of quantum mechanics Βιβλιογραφία * * Ιστογραφία *Ομώνυμο άρθρο στην Βικιπαίδεια *Ομώνυμο άρθρο στην Livepedia *Quantum Mechanics Not in Jeopardy: Physicists Confirm a Decades-Old Key Principle Experimentally ScienceDaily (July 23, 2010) *[ ] Κατηγορία:Νόμοι Κβαντικής Φυσικής